This is a fascinating thought. The models can probably do the same to flag tax loopholes? And no doubt simplifications? Perhaps they can stop the inexorable growth in volume of law and reverse the “wood for trees” problem? @claudeai
We have discovered a substantial number of vulnerabilities in the German legal system using LLMs.
These may enable access to confidential documents, travel without an otherwise required visa, enforceable leave for soldiers at NATO’s JSEC, and more.
Similar to computer systems, the written law can contain vulnerabilities that invite exploitation. In our blog post, we share a selection of vulnerabilities, and present potential exploits for each. To our knowledge, none of these have been previously recorded. We share only those vulnerabilities whose exploitation we believe would not cause serious harm.
blog post: felixringe.com/legal-exploit…
James Samworth retweeted
Every time I hear "10 sigma" event...
BREAKING: Brazil's -19.8% stock market crash on Monday was one of the rarest market events in the last two decades, according to our analysis.
Brazil's EWZ ETF plunged -19.8% on October 26th, marking an 8.4 standard deviation move.
For context, the ETF's average daily move over the last 20 years has been just +0.04%, with a standard deviation of 2.36%.
Under a normal distribution, the probability of a decline this extreme is approximately 1 in 58 quadrillion.
In other words, this event should be virtually impossible under conventional statistical models.
What just happened in Brazil was *almost* impossible.
James Samworth retweeted
Are electricity prices really why the UK and Germany are losing industry to China? Can they be lowered?
British industry pays ~3x what China does for power, German industry ~2x. I rebuilt the bills from published tariffs, 2010–2025. Here's what I found 🧵
James Samworth retweeted
The ugly truth about France and some of the other European countries currently in turmoil - and which none of the politicians want to admit because it'd be political suicide - is that you can't solve the problem by going after immigrants (as the right asserts) or the rich (as the left asserts), but you could solve it by going after the old.
One extraordinary statistic for you: people over 60 in France, a quarter of the population, own 60% of France's wealth, non-financial and financial (ofce.fr/pdf/revue/2025/3-192…).
And here is another crazy statistic:
that same quarter of the population, those above 60, receive nearly two-thirds of all social spending by the French government (previssima.fr/actualite/prot…) - which is famously among the highest in the world (France's government spending is an insane 57.3% of GDP).
Last statistic: they make up about 40% of voters because they're a third of registered voters (insee.fr/fr/statistiques/266…), and they turn out far more than anyone else (franceinfo.fr/elections/sond…).
Put our 3 statistics together and there's almost a bit of an apartheid situation here: the old own most of the country's wealth, collect most of the social spending and have the political power to keep it that way.
Which makes them a de-facto rentier class, living off assets and transfers paid for by younger generations.
And, of course, at the risk of stating a truism, the future is built by the young. Yet France keeps effectively taking money away from them to give it to those whose working lives are already behind them - and need the money far less since they already own the country's wealth.
What about inheritance, I hear you ask? That's the funniest/saddest aspect: given that life expectancy has kept rising, the French now inherit a home at 54 on average. The most common case is someone in their 80s leaving it to heirs in their 50s, in effect the very old transferring wealth to the about-to-be old (insee.fr/fr/statistiques/fic…).
You can add this to our earlier apartheid statement: on top of all the rest, even when the old finally let go of their wealth, it stays within their own "camp".
That's my personal situation, incidentally: I'm 42, my father is 71 and he is starting to look at ways to pass things on to me and my siblings, when our professional lives are already well settled, so it'll arrive when it changes things the least, which is pretty much the French system in a nutshell.
Now, I get that there'd be some unfairness in going after them: they paid into the system their entire working lives, playing by the rules of a social contract that told them if they paid up they'd collect at the end. Changing the rules now means breaking that promise, which is admittedly unfair.
But there's no magic wealth tree in any society: you can only take it where it is. That's the way most major societal transformations end up happening. They're often triggered by a catastrophic event (the so-called "four horsemen": mass-mobilisation war, revolution, state collapse, plague) BUT what really drives change is a transfer: wealth gets pried from the privileged class who've been sitting on it and handed to those who'll build what comes next.
So, in theory and in an ideal world, you can do without the catastrophic event and directly proceed with the transfer...
The fact that in France, and elsewhere in Europe, it's the youth protesting is probably no coincidence - even though they don't frame it as a generational fight. And even though, cruel irony, the left politicians many of them march behind promise to bring the retirement age back to 60 (lcp.fr/actualites/legislativ…), which would make the situation even worse.
Let's say they understand intuitively that the system is stacked against them, even if they haven't yet figured out how. And politicians are obviously doing what politicians do, meaning pandering to the people who actually vote, while pointing the young towards easier - and politically convenient - scapegoats.
To be clear I'm not saying it's the only problem in France, VERY far from it. I'm also not saying that all old people in France live a lavish lifestyle at the expense of younger generations: there are also plenty of very poor retirees who, if anything, would deserve more.
What I am saying is that it's probably the biggest elephant in the room: everyone can see it, nobody dares mention it - no politician, from any side, wants to run on cutting grandma's pension - and it makes every other problem harder to fix.
James Samworth retweeted
totalement d'accord avec Taleb, l'IA est le meilleur filtre à bullshit de l'histoire moderne pour tous ceux dont le métier se résumait à aligner des mots sans jamais penser par eux-mêmes
notez que la panique générale qu'on observe chez les cols blancs en dit long car la plupart découvrent en direct que leur prétendue plus-value professionnelle tenait simplement au fait qu'écrire des rapports creux prenait du temps
ce qu'on vit c'est une purge systémique, tous ceux qui pensaient en formule toute faite se font balayer, tandis que les esprits vraiment vivants, ceux qui créent du chaos, de la poésie et de la stratégie pure…deviennent infiniment plus rares et donc infiniment plus précieux
James Samworth retweeted
The problem isn’t that AI is intelligent. It isn’t. The problem is that too many adults (but not all) are at once mechanistic, imitative, unimaginative, stupid, formulaic, influenceable, & gullible, arrogant beyond their skill set, & too expensive to maintain.
James Samworth retweeted
MIND-BLOWING STATS: A record 2/3 of new cars in China are now electric, while combustion-car sales have fallen by 2/3 since they peaked in 2017
– In 2020, ~95% of sales were combustion-engine cars
– By Sep 2026, they crashed to 33%
– On the flip side, NEVs hit a record 67%
🧵
James Samworth retweeted
The world is getting more of its electricity from renewables but less from nuclear power.
If the world is to reduce its carbon emissions and tackle climate change, it needs to move away from fossil fuels to low-carbon power.
There are two key sources of low-carbon electricity: renewables — which include solar, wind, hydropower and others — and nuclear power.
While rapid growth in solar and wind has increased the amount of electricity coming from renewables, a lack of enthusiasm for nuclear means it’s playing a shrinking role in the global mix.
In the chart, you can see the share of global electricity coming from fossil fuels, renewables, and nuclear since 1985. Since 2000, nuclear and renewables have followed very different trajectories. Back then, both accounted for a similar share of global electricity. But in 2025, renewables made up more than three times as much: 34% compared to 9%.
The total amount of electricity produced by nuclear plants is about the same as it was two decades ago. But because the world produces much more electricity overall, its share of the electricity mix has declined.
(written by @_HannahRitchie and @parriagadap)
James Samworth retweeted
Working with AI models, I've arrived at what I consider the most significant pure-theory breakthrough of my research (in theoretical neuroscience) so far:
arxiv.org/abs/2610.12426
Chaotic systems show what is colloquially called the butterfly effect, namely, a tiny nudge to the initial state grows exponentially in time. How fast the nudge grows depends on its direction. Each direction has its own growth rate, called a Lyapunov exponent, and the full set of rates is the Lyapunov spectrum.
The Lyapunov spectrum is a rich (and diffeomorphism-invariant) characterization of chaos, telling us how many directions are chaotic, how many dimensions the attractor occupies, and how fast the dynamics generate information.
In 1988, Sompolinsky, Crisanti, and Sommers (Physical Review Letters) introduced a nonlinear recurrent-network model of N randomly coupled neurons that becomes chaotic when the coupling strength exceeds a critical value. This network has since become a cornerstone of theoretical neuroscience, both as a model of the spontaneous activity of cortex and as the starting point for training recurrent networks on tasks. I have worked on this model for much of my research.
In the same paper, the authors obtained the largest Lyapunov exponent from the ground-state energy of a Schrödinger equation and named the full Lyapunov spectrum as an open problem. In 2023, beautiful work by Engelken et al. (Physical Review Research) computed the full Lyapunov spectrum numerically. However, an analytical calculation of the full Lyapunov spectrum has remained out of reach.
Four decades after the problem was posed, this paper derives the full Lyapunov spectrum at large N from a simple self-consistent single-site problem.
This calculation has three steps.
First, we lower every exponent by a constant s, which turns the question "how many exponents lie below s?" into the question "how many tangent directions decay?" We show that, if we drive the shifted tangent dynamics with a source and take the minimum-norm solution, the one-step response is the projector onto the decaying directions. Thus, the trace of this projector counts the decaying directions. This step is exact at finite N.
Second, to work with the minimum-norm solution, we cast it as the vanishing-regularization limit of the solution of a least-squares problem. This regularized solution in turn solves a dynamical system with one field running forward in time and another running backward.
Third, we apply the cavity method, that is, we add one neuron to the network, along with its forward and backward fields. The effect of the rest of the network on this neuron then reduces to the classical dynamical mean-field description of the activity of this neuron, plus two kernels that couple the forward and backward fields of this neuron to each other across time. Thus, the full Lyapunov spectrum follows from a single-site problem, which boils down to the self-consistent calculation of these kernels.
The resulting theory agrees closely with simulations for the Lyapunov spectrum, the attractor dimension, and the entropy rate, and recovers known results, including the Schrödinger equation of Sompolinsky, Crisanti, and Sommers for the largest Lyapunov exponent.
As a byproduct, the theory establishes analytically that the chaos is extensive, i.e., the attractor dimension and the entropy rate grow in proportion to N.
I had assumed that this problem was analytically intractable. After working independently for 100 minutes with Max thinking, GPT-6 Astra produced the initial derivation, yielding a self-consistent problem whose solution matched simulations of large networks.
I found this derivation intriguing, albeit complicated and somewhat mysterious (see AI Methodology in the paper). After investigating the structure of the proposed solution more deeply, together with AI models, I arrived at a physically transparent derivation.
I am excited to apply this approach to other network models, trained networks, and, more broadly, to high-dimensional systems to which Lyapunov analysis is relevant, including AI models themselves. Of course, as with any paper, I took care to write up the paper clearly.
A few broader thoughts...
Neural circuits are high-dimensional nonlinear dynamical systems, and such systems are notoriously hard to understand. I would frame the central problem of theoretical neuroscience as understanding how such systems function, process information, learn, and generate behavior.
Many people in the theoretical sciences are anxious about AI. However, in my field at least, we are nowhere close to fully understanding the high-dimensional computations unfolding in our brains. With AI, we could reach a level of understanding that so far we have only gestured toward. So, I am excited.
James Samworth retweeted
If confirmed, this is telling: Russian data centres get hit, and online activity around AfD suddenly plummets. 📉
So much talk about German patriotism… then the connection from Russia goes down. 🤔🇷🇺
James Samworth retweeted
Nothing says" I've got my life together" like 1,000 lbs of salmon-fueled confidence.
This sounds a big one… #ElNiño apple.news/AQfWQ21aHTkqzHprI…
James Samworth retweeted
Terence Tao just posted this really insightful thread which seems to have been written in reaction to the Navier Stokes announcement. Please give it a read. mathstodon.xyz/@tao/11723732…
We’re sharing a solution to the Navier-Stokes Millennium Prize Problem, one of the deepest problems at the frontier of mathematics.
The proof was produced by a group of agents, using an OpenAI next-generation model significantly more capable than GPT-6 Astra.
The problem concerns whether the description of smooth three-dimensional fluid motion modeled by the Navier-Stokes equations can break down. It has remained unresolved for roughly 90 years.
We are focusing on understanding this model, and using what we learn to help us guide and pace how we pursue further advances in capability.
Our goal is to build AI systems which are steerable, accountable, and connected to people, which may require more deliberate choices about the pace of progress, as we continue our mission to ensure AGI benefits all of humanity.
openai.com/index/navier-stok…
James Samworth retweeted
I wanted to speak - for the first time in detail - about NARCISSISTIC CONTRARIANISM.
This is a trait Trump has shown with greater frequency in recent days. It's led some analysts to surmise that Trump is acting as if he wants to lose the midterms. Here's what it REALLY is:
A narcissist contrarian is someone who takes the opposite side of obvious or even popular issues, opposing prevailing views. They do this reflexively, because they are feeling enfeebled or attacked.
When the story of the excessive time at sea by military personnel aboard the USS Lincoln was driving public ridicule, Trump characterized their time at sea as "not long enough." Why would he possibly say that? When a bad inflation report broke, Trump was quoted as saying "I love inflation." Really? He's said the same thing recently about "data centers," a sensitive topic across the political spectrum. And any time he is accused of too much focus on the WH ballroom, a broadly unpopular issue, his response is to speak glowingly and lavishly about it even more.
The key thing to realize here is that a narcissistic contrarian doesn't oppose prevailing views because they've thought something through. On the "contrary."
They do it because disagreement serves their battered ego, signals grandiosity through them knowing better, and attracts attention, which is a narcissist's nutrition.
Psychologists speak to 8 core traits leading a narcissist to become excessively contrarian which are:
1. A grandiose self-image that has taken a battering.
2. An innate resistance to compromise.
3. Binary thinking - if one is right, the other is wrong.
4. Deep insecurity masked by professing superiority.
5. The need for self-preservation - to appear smarter - now, to reverse the trend where they appear old or ill.
6. Deep feelings of innate distrust - assuming bad intent even where none exists; paranoia.
7. The need to re-exert autonomy - show they can and will do what they want, to dominate a news cycle.
8. The need to prevail in a big current power struggle.
Let me help you go through that list: CHECK, CHECK, CHECK, CHECK, CHECK, CHECK, CHECK, and CHECK.
So - to summarize - when Trump takes a position or makes a statement that goes against conventional wisdom, it's not only because he's ignorant, stubborn, or an idiot - it's because he's losing, desperate, and narcissistically damaged - and suggesting or adopting a contrary viewpoint is his way of trying to cope, reverse bad trends, and nurse his narcissistic injury.
James Samworth retweeted
VO2 max drops 46% from age 20 to 70, but cardiac output only falls 31%. The gap between those numbers reveals something unexpected about where aging really happens.
For decades, the dominant explanation for declining aerobic capacity with age centered on the cardiovascular system. Your heart beats slower, pumps less blood per beat, and delivers less oxygen to working muscles. This narrative made intuitive sense and aligned with the most visible changes of aging.
But new research quantifies a different story. The limitation isn't just about oxygen delivery. It's increasingly about what happens after the blood arrives at muscle tissue.
VO2 max represents the maximum rate your body can consume oxygen during all-out exercise. It's one of the strongest predictors of longevity and functional independence as we age. Beginning around age 30, it drops roughly 10% per decade in sedentary people.
The Fick equation breaks down what determines VO2 max:
VO2 max = Cardiac Output × Arteriovenous Oxygen Difference
Cardiac output is how much blood your heart pumps per minute. The arteriovenous oxygen difference, or a-vO2 difference, measures how much oxygen your muscles extract from that blood.
This equation splits the aging story into two parts: central factors (heart and lungs delivering oxygen) and peripheral factors (muscles extracting and using oxygen).
Central limitation comes from declining maximal heart rate, which drops about one beat per minute per year after age 20, and reduced stroke volume as the heart stiffens and large arteries lose elasticity.
Peripheral limitation comes from changes in skeletal muscle itself: mitochondrial density and function, capillary networks that deliver blood to muscle fibers, muscle mass, and the enzymes that drive oxidative metabolism.
The new analysis reveals that by late middle age, nearly half of the limitation on VO2 max originates in the periphery, not the cardiovascular system.
In younger adults, approximately 77% of the total limitation is central and 23% peripheral. Your heart and oxygen delivery system are the primary bottleneck.
In older adults, that shifts to roughly 56% central and 44% peripheral. The muscles are catching up to the heart as a source of failure.
The most striking finding: oxygen extraction capacity falls dramatically with age. Skeletal muscle extracts roughly 80% of delivered oxygen at maximal effort in young adults. By ages 75 to 80, that figure drops to approximately 60%.
That's a 20 percentage point decline in the muscle's ability to use the oxygen the cardiovascular system is still delivering.
Four converging biological processes drive this peripheral decline:
1. Sarcopenia preferentially strips away type II muscle fibers, which are rich in mitochondria and oxidative capacity. You lose not just muscle mass, but specifically the muscle tissue most capable of using oxygen.
2. Mitochondrial density and efficiency decline. Mitochondria become fewer in number, smaller in size, and less effective at converting oxygen into usable energy through ATP production.
3. Capillary rarefaction thins the networks of small blood vessels threading through muscle tissue. Fewer capillaries mean longer distances for oxygen to diffuse from blood to muscle cells, creating a bottleneck at the delivery endpoint.
4. Interstitial changes in the space between capillaries and muscle cells further impair oxygen movement. Changes in tissue structure and composition slow the final step of oxygen's journey into working muscle.
None of these is catastrophic alone. Together, they compound into something substantial that previous research underemphasized by focusing primarily on cardiac decline.
Here's what matters for intervention:
• The peripheral factors driving VO2 max decline (mitochondria, capillaries, oxidative enzymes) remain responsive to training well into later decades of life
• Endurance training produces the most reliable capillary growth: 13.3% increase in capillary density and 15% increase in capillary-to-fiber ratio over 8-10 weeks
• High-intensity interval training (HIIT) delivers comparable mitochondrial gains to endurance training but requires substantially less total time, estimated at 1.7x more time-efficient
• Sprint interval training (SIT) generates the fastest mitochondrial signal per minute of any modality, producing 3-5x greater VO2 max improvement per hour of exercise, though it doesn't significantly increase capillary density
• Meaningful adaptation begins within two weeks. Roughly 13.7% of total mitochondrial gains from an endurance block occur in the first 14 days
• The biological machinery that aging erodes is the same machinery that training can partially rebuild, even in the seventh and eighth decades of life
The practical implication: maintaining VO2 max with age isn't just about keeping your cardiovascular system fit. You need training that specifically targets peripheral adaptations, the cellular machinery inside muscle tissue that extracts and uses oxygen.
That means prioritizing exercise intensity that creates metabolic stress sufficient to trigger mitochondrial remodeling and capillary growth. Moderate-intensity steady-state exercise improves cardiovascular fitness but generates weaker peripheral adaptation signals than high-intensity work.
The framework also explains why training becomes more important, not less, as you age. When you're 25 and 77% of your VO2 max limitation is central, peripheral decline happens quietly in the background. By 65, when peripheral factors account for nearly half the limitation, those quiet changes have accumulated into the primary driver of functional decline.
The decisions made in the fourth and fifth decades of life shape the physiological ceiling of the seventh and eighth. Aerobic aging is a slow, cumulative process affecting multiple systems simultaneously. So is the adaptive response to training.
The most important variable isn't the perfect training modality. It's consistency across the decades during which the oxygen cascade is quietly remodeling in one direction or the other.
James Samworth retweeted
Top 10 Spreaders of Disinformation in the US according to ChatGPT:
1. Donald Trump
2. Fox News
3. Elon Musk
4. Robert F. Kennedy
5. Alex Jones
6. Tucker Carlson
7. Sean Hannity
8. Newsmax
9. The Gateway Pundit
10. Breitbart
James Samworth retweeted
A selection of articles published by The Spectator between August 01 and August 14 2026:
BREAKING: Jason Arday, the former University of Cambridge professor, has been found dead at an address in Battersea, according to reports.
A spokesperson for the Metropolitcan Police said the 41-year-old's death is not being treated as suspicious.
“Sadly, a 41-year-old man was pronounced dead at the scene. His next-of-kin have been informed and are being supported by officers," he said.
“At this time his death is being treated as unexpected, but is not believed to be suspicious.
"The case is being investigated by officers from the Met’s Central South Command Unit. A file will be prepared for the coroner.”
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